Abstract: We introduce hierarchical neighbor graphs, a new architecture for connecting
ad hoc wireless nodes distributed in a plane. The structure has the flavor of
hierarchical clustering and requires only local knowledge and minimal
computation at each node to be formed and repaired. Hence, it is a suitable
interconnection model for an ad hoc wireless sensor network. The structure is
able to use energy efficiently by reorganizing dynamically when the battery
power of heavily utilized nodes degrades and is able to achieve throughput,
energy efficiency and network lifetimes that compare favorably with the leading
proposals for data collation in sensor networks such as LEACH (Heinzelman et.
al., 2002). Additionally, hierarchical neighbor graphs have low power stretch
i.e. the power required to connect nodes through the network is a small factor
higher than the power required to connect them directly. Our structure also
compares favorably to mathematical structures proposed for connecting points in
a plane e.g. nearest-neighbor graphs (Ballister et. al., 2005), $\theta$-graphs
(Ruppert and Seidel, 1991), in that it has expected constant degree and does
not require any significant computation or global information to be formed.